Figure P5.2 shows a PCM wave in which the amplitude levels of +1 volt and -1 volts are used to represent binary symbols 1 and 0 respectively. The codeword used consists of three bits. Find the sampled version of an analog signal from which this PCM is der
IProblem 3.1.11
a) Determine the function f(t) whose Fourier transform is shown in figure P-3.l.a.
b) Determine the function f(t) whose Fourier transform is shown in figure P-3.l.b.
c) Sketch f (t) and g (t) near t = 0. What effects does the phase has on
ECE 318 - Communication Systems
Winter 2017
HW1; Signals and Systems: Solutions
Problem 1 (Haykin 2.4)
Be careful that the figure in the book uses f [Hz] as its frequency variable, whereas we
conventionally use [rad/s] in this course. If we want to use th
ECE 318 - Communication Systems
Winter 2017
HW2; Amplitude Modulation 1: Solutions
Problem 1 (Haykin 3.2 (a,b,c)
h
i
(a) We know i = I0 exp(
)
1
. Using the Taylor series expansion of exp(x) up to the
VT
third order term, which is:
exp(x) = 1 + x +
x2 x3
ECE318 Mathematical Background
Preamble
The following are mathematical concepts and questions that have appeared in previous offerings of the
ECE 318 course. Solving these questions can help you to self-assess your preparation for this course
as well as p
ECE318 Mathematical Background
Preamble
The following are mathematical concepts and questions that have appeared in previous offerings of the
ECE 318 course. Solving these questions can help you to self-assess your preparation for this course
as well as p
ECE 318 - Communication Systems
Winter 2017
HW2; Amplitude Modulation 1: Problems
Problem 1 (Haykin 3.2 (a,b,c) In part b, instead of determining the spectrum, only determine the frequencies that are present after expanding i from part a.
Problem 2 (Hayki
ECE 318 - Communication Systems
Winter 2017
HW1; Signals and Systems: Problems
Problem 1 (Haykin 2.4. Note that arg |G(f )| should be arg G(f ) in Figure P2.4)
Problem 2 (Haykin 2.10)
Problem 3: Determine if each of the following signals is periodic. If a
Problem 4.1.1
Consider the cosine wave
g (t) = A cos(2 f0t)
Plot the spectrum of the discrete-time signal g (t) derived by sampling g (t) at the times tn = n=fs , where n = 0 1 2 and (i) fs = f0 (ii) fs = 2f0 (iii) fs = 3f0
Solution
g (t) = A cos(2 f0t) G
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ECE 318 - Communication Systems
Winter 2015
Tutorial 7: Angle Modulation (Part 2)
Review
Its been three weeks since the last tutorial, so lets review some things rst.
An angle-modulated signal is generally given by
(t) = A cos(i (t)
For phase modulation w
ECE 318 - Communication Systems
Winter 2015
Tutorial 8: Sampling
Note that the rst half of the tutorial was used to nish the problem on frequency multipliers
from Tutorial 7; the last 10-15 minutes of this tutorial were also used to hand back midterms,
so
ECE 318 - Communication Systems
Winter 2015
Tutorial 2: Signals and Systems
Problems
Problem 1
Suppose we have the following LTI system:
x(t)
d
dt
+
y(t)
Let x(t) be a square wave with T = 2:
1
1
rect t nT
x(t) = +
2 n=
2
0.5
3
2
1
0
1
0.5
(a) Find the p
ECE 318 - Communication Systems
Winter 2015
Tutorial 6: Angle Modulation (Part 1)
Review
Angle modulation uses a lot of denitions, so lets review them rst.
An angle-modulated signal is generally given by
(t) = A cos(i (t)
Where i (t) is called the instant
ECE 318 - Communication Systems
Winter 2015
Tutorial 5: Amplitude Modulation (SSB and VSB)
Problems
Problem 1 (Haykin 3.19)
Shown below is a Weaver modulator, which allows us to generate single-sideband modulated
signals without explicitly taking the Hilb
ECE 318 - Communication Systems
Winter 2015
Tutorial 3: Amplitude Modulation (DSB-LC)
Problems
Problem 1
Consider the following DSB-LC modulator. Let the bandwidth of f (t) be B [rad/s]. Assume
the following:
c
B
maxcfw_f (t) = mincfw_f (t) = 1
k is a pos
ECE 318 - Communication Systems
Winter 2015
Tutorial 4: Amplitude Modulation (DSB-SC and QCM)
Problems
Problem 1
Two signals f1 (t) and f2 (t) with corresponding spectra shown below are to be transmitted simultaneously over a channel using frequency divis
ECE 318 - Communication Systems
Winter 2015
Tutorial 1: Review of Signals and Systems
Fourier transform
In this course, we will be using the following convention for the Fourier transform and its
inverse:
f (t)ejt dt
F () = Fcfw_f (t) =
f (t) = F
1
1
cfw_
ECE318: Communication Systems, Fall 2011
Department of Electrical and Computer Engineering, University of Waterloo
Instructor: Prof. Zhou Wang
Homework 2
Problem 1
Problem 2
Problem 3
Problem 4
A sinusoidally modulated DSB-LC waveform
1
cos
cos
is applied
ECE318: Communication Systems, Fall 2011
Department of Electrical and Computer Engineering, University of Waterloo
Instructor: Prof. Zhou Wang
Homework 4
Problem 1
Let the random process
be defined by
random variables, each uniformly distributed on
, wher
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